THE FINITE VOLUME METHOD FOR AN ELLIPTIC-PARABOLIC EQUATION
R. EYMARD, M. GUTNIC and D. HILHORST
Abstract.
In this note we prove the convergence of a finite volume scheme for the discretization of an elliptic-parabolic problem, namely the nonlinear diffusion equation $c(u)_t-\Delta u = 0$, together with Dirichlet boundary conditions and an initial condition. This is done by means of a priori estimates in $L^2$ and the use of Kolmogorov's theorem on relative compactness of subsets of $L^2$.
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